Bulletin of the
Korean Mathematical Society BKMS

We introduce two kinds of quasi-inner functions. Since every rationally invariant subspace for a shift operator $S_K$ on a vector-valued Hardy space $H^{2}(\Omega,K)$ is generated by a quasi-inner function, we also provide relationships of quasi-inner functions by comparing rationally invariant subspaces generated by them. Furthermore, we discuss fundamental properties of quasi-inner functions and quasi-inner divisors.

Keywords: a generalized Beurling's theorem, Hardy spaces, quasi-inner functions, rationally invariant subspaces

MSC numbers: 47A15, 47A56, 47B37, 47B38